Estimation of the Undervaluation of the Chinese Currency by a Non-linear Model

Transcription

1 Estmaton of the Undervaluaton of the Chnese Currency by a Non-lnear Model Gene Hsn Chang a* a Shangha Unversty of Fnance and Economcs and Unversty of Toledo Abstract Ths paper conducts a quanttatve estmaton for the equlbrum value of the Chnese currency, the RMB, by a non-lnear model, after control of the Balassa-Samuelson effect. The model provdes a better ft for the valuaton of the Chnese currency than the conventonal lnear or log lnear Rogoff models. The model regresson s robust. Our regresson reveals that the RMB was undervalued by 32% n 2004, but further ncreased to 35.8% n 2005 because the Balassa- Samuelson effect dmnshes as Chna s economy surges. These fgures suggest that the extent of undervaluaton of RMB s more substantal than most prevous estmates, whch range from 15% to 27.5%. The estmates of the model provde mportant nformaton about the lkely changes n the value of the RMB n the near future. JEL Classfcaton: F31, C31 Keywords: Chna, currency value, exchange rate, estmaton 1. Introducton The equlbrum value of the Chnese currency, the RMB, has become both an academc and poltcal subject n the past several years. There have been several dfferent estmates of the true value of RMB. Goldsten and Lardy (2003) suggest that the RMB s undervalued by 15 to 25% n Chang and Shao (2004) estmate an undervaluaton of 22.5% n 2003 by usng a lnear model wth a control of heteroskedastcty. Frankel (2004) uses a double log lnear model and found that the RMB was 36% undervalued n The US Senate bll sponsored by Charles Schumer (Democrat New York) and Lndsey Graham (Republcan South Carolna) n 2005 mplctly assumes that the RMB s 27.5% undervalued, thus callng for a puntve duty of the same level of 27.5% on Chnese mports. Each of the above estmates has some shortcomngs. Goldsten and Lardy (2003) gve a range for possble equlbrum values of yuan wthout a rgorous model or detals on how they obtaned the fgures. Chang and Shao (2004) and Chang (2007) use a * Emal: genechang@bex.net. Tel (US): or The author would lke to thank Bll Kosteas, Hazhou Huang, anonymous referees and others for ther valuable comments.

2 30 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) lnear model, but the actual relatonshp of the regresson model seems to be non-lnear. Frankel (2004) uses a log lnear model, called the Rogoff model. The model regresses the log real exchange rate (RER) on the log per capta ncome. However, as we wll show, estmates from the Rogoff model turn out to be even worse than those from a smple lnear model. In ths paper I wll suggest a new non-lnear model for regresson that fts the dstrbuton of the observatons better than ether the lnear or the Rogoff models. In the followng secton, I wll dscuss the data, set up the regresson model, provde the estmates, and dscuss the results. Secton 3 concludes. 2. Model and Estmaton There are three basc approaches conventonally used to estmate the equlbrum value of a currency. The frst s based on the supply and demand of the foregn exchanges. Ths type of study focuses on the trade and current account surpluses or defcts to fgure out the equlbrum value of the currency. The result from ths approach s, at best, the short-run market equlbrum value of the currency. Ths short-run value s dfferent from the long-run equlbrum value, whch s what the currency value s supposed to converge towards. The second approach s to estmate the changes n relatve purchasng power party (PPP). The problem wth ths approach s that the researcher must start wth a benchmark year, whch s usually assumed to be a tme perod n whch the exchange rate s n equlbrum. Ths approach cannot be used to estmate the Chnese currency value, because Chna has never been n a market system n the past, and there are no such benchmark years for an equlbrum exchange rate. The thrd approach s usng the absolute PPP. Ths s more relable and less controversal. Fewer studes n the past adopted ths approach because the data for absolute PPP were more dffcult to obtan than the data needed for calculatng relatve PPP. However, the data are now readly avalable. The World Development Indcator by the World Bank publshes both the GDP fgures n exchange rate and the GDP fgures n PPP for dfferent countres. The mplct PPP can be derved from the dfference between the two fgures. The US dollar s used as the nternatonal currency unt, and thus the common denomnator. We let e stand for the nomnal exchange rate of a country s (ncludng Chna s) currency for a dollar, that s, the country s own currency prce of a US dollar. We let p stand for the country s domestc prce level, and p * for the US prce level. The real exchange rate (RER) of the country s currency s RER = ep* p. In a frctonless PPP economc world wth equal productvty across all sectors wthn each country, the real exchange rates of all countres would be the same. However, the Balassa- Samuelson effect argues that the dfference n productvty between rch and poor countres n the tradable sector may be large, but the dfference s much smaller n the non-tradable sector; hence, the RER would be hgher n poorer countres. 1 In other words, currences n the poorer countres tend to be undervalued unless we correct the 1 See Samuelson (1964). Scholars often consder that the ncome level, or GDP per capta, s used as the proxy for the total factor productvty n the Balassa-Samuelson theory.

3 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) raw data by removng the Balassa-Samuelson effect. To estmate the equlbrum value of a currency, one should take nto account the Balassa-Samuelson effect. A common practce to remove the Balassa-Samuelson effect n an emprcal work s regressng the RER across all countres on per capta GDP. 2 Further, as Frankel (2004) suggested, the devaton from ths regresson lne reflects the currency s over- or undervaluaton. The mpled argument for ths approach s that, for countres whch are engaged n trade, t cannot be a case that all currences are overvalued (or all are undervalued). Frankel dd not provde a theoretcal model for ths approach; however, to respond to a queston rased by an anonymous referee, n the appendx of ths paper I provde a smple theory, frst, to justfy usng the mean of RERs as the equlbrum value; and secondly, to justfy why the devaton of an RER from the mean measures the over- or under-valuaton of an currency. Fgure 1 plots the RER aganst the ncome levels of 160 countres n 2001, whch are avalable n the World Development Indcator. Chang (2007) and Chang and Shao (2004) adopt a lnear functon specfcaton, RER = a + b GDPpc = ε, where GDPpc stands for the GDP per capta, and ε the error term for country. After a further control of the heteroskedastcty, Chang and Shao obtan the predcted RER at varous per capta ncome levels. Table 1 replcates ther results. It provdes a comparson of the valuaton of dfferent currences n the world. Fgure 1 10 Real Exchange Rate (RER) of Varous Countres Real Exchange Rate RER Regresson lne GDP per capta (1,000 US$) OLS Coeffcents Standard Error t Stat Observatons 160 Intercept Sum of Square Errors GDPpc/ See Rogoff (1996).

4 32 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) Table 1 Real Exchange Rate (RER) of Selected Currences (2001) by a Lnear Regresson wth a Control of Heteroskedastcty Parameters a b c d Estmates Country Per capta GDP 2001 Real Exchange Rate Actual Predcted Over(+) Under(-) valued P-value Kyrgyz Republc % Belarus % Camboda % Congo, Dem. Rep % Inda % Ukrane % South Afrca % Vetnam % Bulgara % Chna % Bangladesh % Phlppnes % Indonesa % Italy % Thaland % Russan Federaton % Hungary % Hong Kong, Chna % Fnland % France % Sweden % Unted Kngdom % Korea, Rep % Japan % Kuwat % Saud Araba % Zamba % Venezuela, RB % Congo, Rep % Note: Ths table replcates Table 1 of Chang and Shao (2004). The data was from WDI onlne 2003, hence the actual RER for Chna s slghtly dfferent from the other tables whch are based on the WDI onlne Fgure 1 plots the 160 observatons n the sample wth the lnear ftted lne. One can see from Fgure 1 that the relatonshp between RER and ncome s not lnear, but rather,

5 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) a non-lnear curve. Frankel (2004) adopts a double log form specfcaton suggested by Rogoff: ln RER = a + bln GDPpc + ε to estmate the undervaluaton of RMB. Fgure 2 shows the curve from the regresson and the observatons. Whle the Rogoff specfcaton s non-lnear, t does not seem to be a better ft than the lnear curve. The regresson results appear to be out of lne. For nstance, t says that n 2003, Chna s currency RMB s 196% undervalued. The second last column of Table 3 from the rght shows all of the estmaton results from the Rogoff model Fgure 2 Ftted Regresson Lne by the Rogoff Specfcaton Predcted Actual Real Exchange Rate GDP per capta pc (1,000 US$) Regresson Functon: log RER = a + b log GDPpc/1000 Observaton: 160 Coeffcents a b Sum of Squared Errors of the log RER values: Sum of Squared Errors of the true values*: *Note: To obtan ths value, we frst recover the predcted true value of RER, then obtan the sum of squared errors between the actual and true predcted values of RER. In ths study, I suggest a new specfcaton for the relatonshp between RER and per capta ncome level as follows: 1 RER c ( a b GDPpc ) = (1) The equaton s relatvely smple wth only three coeffcents to be estmated. The error term ε s assumed to be ndependently and normally dstrbuted. So the Maxmum

6 34 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) Lkelhood Estmaton (MLE) maxmzaton provdes consstent estmates, even f heteroskedastcty exsts. The model s qute robust n searchng for the optmal values of the coeffcents by MLE from varous ntal values. At the same tme, t also fts the dstrbuton of the RER data very well. To estmate, we use the sample n Chang and Shao (2004), whch ncludes only the country data from 2001 provded by the World Bank. 3 Ths sample stll conssts of 160 observatons, whch s large enough for meanngful estmaton. Because we use only data from 2001, we avod addng dummy varables for the possble structural shfts over tme perods. We use the MLE method to obtan consstent estmates for the coeffcents a, b and c. Then we use the estmates to obtan the predcted values, whch leads to the regresson curve. Fgure 3 plots the regresson curve along wth the orgnal observatons. The coeffcent estmates of the regresson are lsted at the table at the bottom of Fgure Fgure 3 The New Regresson Model Predcted Actual Real Exchange Rate GDP Per Capta (1,000 US$) Regresson functon: RER = c + (a + b GDPpc/1000)^(-1) + ε Observatons 160 Sum of squared errors: Estmated coeffcents a b c WDI onlne, Oct. 2003, the World Bank

7 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) We use the Quas-Newton algorthm to do the MLE optmzaton. The model s robust n varous ntal values. In optmzaton, I set the non-negatve bounds for the three estmates. In theory, the coeffcent c s supposed to be around 1. That s, the RER s supposed to be 1 when GDPpc s approachng nfnty. However, the regresson results measured by SSE turn out to be worse when the low bound s set to 1 than when the low bound s set to less than 1. After several trals, the lower bound s set to 0.1. The SSE does not mprove notceably beyond ths level. The ft by the regresson turns out to be qute good wth ths setup of restrctons. From Fgure 3, one can see that the proposed functon approaches 1 at an ncome level of about US$40,000, whch s the upper lmt of the GDP per capta n the current world. Ths mples that the proposed functon s powerful, but may be lmted to a certan range of ncome levels (say, below the US$40,000 GDP per capta level). A further refnement of the functon beyond the per capta ncome level of US$40,000 can be a pecewse functon that conssts of another functon when ncome s beyond US$40,000. Yet ths s beyond the ncome range we are concerned wth here. From a comparson among the three fgures, one can see that the new specfcaton provdes a better ft to the dstrbuton of the observaton. Ths s ndeed proved to be the case when we compare the sum of squared errors (SSE) of the three regressons. The Rogoff double log model s the worst, wth a value of SSE of The straght lnear model has the value of SSE of The new non-lnear model reduces the SSE to Apparently, the new specfcaton n ths study offers a better descrpton of the relatonshp between RER and the per capta ncome level. We then use the estmated model to obtan the predcted RER for Chna by the estmated coeffcents, whch are shown n Table 2. The last column of Table 2 present the estmated overvaluaton (+) or undervaluaton (-) of RMB. Table 2 Real Exchange Rate of Chna Real Exchange Rate Year Per capta GDP 2001 Actual Predcted Over(+) Under(-) valued % % % % % % % % % % % % % %

8 36 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) % % % % % % % % % % % % % % % % 2005* % * estmates Sources of data: For perod from , from WDI on lne, Aprl 2006 Data after 2003 are adjusted by usng the updated nformaton from Chnese Statstcal Bureau Webste Database. It can be seen that RMB had been overvalued pror to 1991, but has been undervalued snce that year. The undervaluaton has become more substantal snce the begnnng of ths century. The undervaluaton of the RMB aganst the dollar reached 35.3% n 2003 and 32.0% n What s nterestng s that n 2005 the undervaluaton ncreased to 35.8%, although the Chnese authorty revalued the nomnal exchange rate by more than 2% n Durng 2005 Chna s GDP nflaton rate s 3.7%, slghtly hgher than that n the US (3.1%). Addng the nomnal revaluaton, the Chnese currency actually had a real revaluaton n The reason the undervaluaton even ncreased durng the same year s because the rapd growth n Chna caused the Balassa- Samuelson effect to dmnsh n our regresson model. Durng the past four years, the US and many other countres have pressed Chna to revalue ts currency whenever a trade dspute arose wth Chna. Our emprcal test reveals that, regardless of whether or not the revaluaton would help reduce ther trade defcts wth Chna, the argument that the RMB was undervalued s vald. Whle our estmates support the argument that the Chnese currency s undervalued, the fgures need to be nterpreted wth cauton. The estmates are subject to all possble random errors from the data sample and other possble statstcal problems. To make a comparson of the emprcal results from dfferent models, Table 3 presents the estmates for the undervaluaton of RMB from four dfferent models n one table. The Rogoff double log model does not provde convncng results, as t shows that the RMB has been undervalued by more than 100% snce Ths result s dfferent from the other three models. The results of the OLS lnear model and that of

9 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) the lnear model wth a control of heteroskedastcty are consstent among themselves. The new non-lnear model s also n lne wth the lnear models n terms of the trend of the changes n the valuaton of RMB, although the numercal values are qute dfferent n some years. Overall, these fgures of the three models (except the Rogoff model) provde some consstent nformaton about the state of RMB valuaton. Table 3 Comparson of the Estmates of Undervaluaton from Varous Models Lnear Year OLS control of heteroskedastcty Rogoff Log model New nonlnear model % 66.7% 41.0% 74.0% % 64.8% 35.0% 71.3% % 65.5% 34.0% 71.0% % 51.3% 6.2% 59.2% % 50.8% 7.2% 59.8% % 44.9% -2.8% 55.8% % 40.2% -16.2% 50.1% % 36.8% -29.7% 44.6% % 38.5% -34.5% 42.9% % 33.8% -45.6% 38.7% % 33.3% -46.2% 38.8% % 19.7% -70.2% 28.9% % -8.9% % 8.9% % -13.6% % 7.2% % -4.4% % 9.7% % -5.0% % 6.0% % -11.2% % -1.4% % -19.7% % -9.3% % -35.2% % -26.1% % -24.3% % -18.1% % -12.6% % -7.4% % -7.4% % -4.8% % -6.1% % -7.1% % -8.9% % -13.7% % -14.3% % -19.5% % -18.4% % -23.5% % -20.1% % -28.0% % -23.2% % -32.7% % -22.5% % -35.3% % -19.2% % -32.0% 2005* -11.5% % -25.3%

10 38 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) Concludng Remarks In ths paper, we suggest a non-lnear specfcaton for estmatng the long-run equlbrum value of the RMB, after controllng the Balassa-Samuelson effect. Our model provdes a much better ft for the data than the prevous models, ncludng the lnear model and the Rogoff double log model. The Rogoff model was rejected because t fals to provde a good ft for the data and t does not provde convncng estmates about the valuaton of the RMB aganst the US dollar or nternatonal currences. The estmates for the valuaton of the RMB from the lnear model are generally consstent wth the consensus about the valuaton of the RMB. However, the relatonshp between the per capta ncome level and RER s apparently non-lnear. Hence, the lnear model does not ft the dstrbuton of the data well, especally for those observatons far away from the mean of the per capta ncome. Estmates for the undervaluaton of RMB by our new non-lnear model are generally consstent wth the results of the lnear models, but the results are more accurate because the non-lnear model descrbes the mpled relatonshp better and has a much better ft for the world data. Our results, reported n Table 2, show that the RMB was overvalued n the 1970s and 1980s, but undervalued n the 1990s and 2000s. Admttedly, the predcted fgures n 1970s and 1980s are less accurate, snce the economc structure n those perods were lkely dfferent from that n 2001, the year from whch we obtaned the estmated parameters. However, these predcted fgures stll seem to ft conventonal belefs about the dynamc changes n the RMB values. We see that the RMB was substantally overvalued pror to In 1986 Chna ntroduced the dual track exchange rate regme, and at the begnnng of 1994, Chna unfed the exchange rates. Ths explans why the RER abruptly changed n those two years. After 1998, undervaluaton has tended to ncrease. Two forces are behnd ths trend. Frst, the RER grew due to low nflaton or even deflaton durng ths perod n Chna. Secondly, the predcted RER declned because of rapd economc growth. Our results show that the RMB has been undervalued n the range of 25% to 36% n the past four years. Ths seems to confrm the general opnon of the extent of undervaluaton of RMB, such as by Lardy and Goldsten or by the US Congress. In July, 2005, Chna announced ts abandonment of the ad hoc dollar-peg exchange rate system; snce then, Chna has allowed the RMB to adjust wthn a moderate range to respond to market forces. As a result, the RMB has steadly revalued. Yet, because the government stll ntervenes heavly, the revaluaton has been very lmted. The RMB revalued cumulatvely only by 3.2% from the prevous 8.27 yuan to one dollar n July 2005, to 8.01 yuan to one dollar n Aprl Ths extent of revaluaton s certanly too small to satsfy the market pressure. What s the future of the RMB? On one hand, we can antcpate two forces that wll push for a real revaluaton of RMB or a reducton of the extent of undervaluaton of RMB. The frst force s nomnal revaluaton. The second force s an nflaton rate n Chna greater than that n the US. The undervaluaton of RMB wll lead to a foregn captal nflow, thus causng the monetary base to ncrease and addng pressure to the prce level. The surge n prces of new houses and constructon materal n Chna durng the perod of 2003 and 2004 s an example to confrm ths theory. For nstance, n 2005,

11 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) the nflaton rate measured by the GDP deflator n Chna was 3.8%, hgher than that n the US. Ths dfference n the nflaton rates has effectvely revalued the RMB n real terms. On the other hand, we also antcpate a counterforce aganst a real revaluaton of RMB. As the Chnese economy grows and GDP per capta ncreases, the Balassa- Samuelson effect dmnshes. Hence, ceters parbus, the estmated undervaluaton of RMB by our model wll ntensfy. The net result of the change n valuaton of the RMB wll depend on the relatve magntudes of these postve and negatve forces. However, one can expect that market force wll domnate once the RMB moves to a more flexble regme; hence, we can be confdent n predctng that the revaluaton of RMB s the trend for the near future. References Chang, G.H., 2007, Is the Chnese Currency Undervalued? Emprcal Evdence and Polcy Implcaton, The Internatonal Journal of Publc Admnstraton 30, Chang, G.H. and Q. Shao, 2004, How Much Is the Chnese Currency Undervalued? A Quanttatve Estmaton, Chna Economc Revew 15, Frankel, J., 2004, On the Renmnb: The Choce Between Adjustment under a Fxed Exchange Rate and Adjustment under a Flexble Rate, wrtten for a Hgh-level Semnar on Foregn Exchange System, Dalan, Chna, May 26 27, A verson s avalable onlne: Goldsten, M. and N. Lardy, 2003, Chna s Exchange Rate Regme, Asan Wall Street Journal, September 12. Rogoff, K., 1996, The Purchasng Power Party Puzzle, Journal of Economc Lterature 34, Samuelson, P.A., 1964, Theoretcal Notes on Trade Problems, Revew of Economcs and Statstcs 46,

12 40 Gene Hsn Chang Asa-Pacfc Journal of Accountng & Economcs 15 (2008) Appendx The Devaton of RERs from the Mean Measures the Extent of Over- or Undervaluaton In what follows we provde a smple justfcaton for usng the mean value of RERs of all countres as the equlbrum value, and, the devaton from the mean s nterpreted as the extent of over- or under-valuaton. Let us start wth a smplfed model, so we can focus on the core ssue. Assume that there are n countres engaged n trade, all are of the same economc sze and at the same ncome level. Country s trade (or, current account balance) s a functon of ts overvaluaton or undervaluaton. In partcular, we set up: T = a(rer RER*) where T s the trade balance of country. RER * s the equlbrum real exchange rate. RER s the real exchange rate of country, and a s a constant. If country s currency s undervalued, thus RER RER * > 0, then T > 0. The country runs a trade surplus. If the country revalues ts currency to return to the equlbrum level thus RER RER * > 0, then ts trade s n balance, T = 0. Conversely, f ts trade s not balanced, ts currency s not at the equlbrum level. These arguments are straghtforward n nternatonal economcs. Summarze all countres trade, and note that t must be globally balanced: T = 0. We have n then, n T = a (RER RER * ) = 0 RER = n RER * then we have the equlbrum real exchange rate RER * s determned by, 1 RER * = n RER Now we see that the equlbrum exchange rate s the mean of the real exchange rates. Further, the dfference between RER and RER *, RER RER *, measures the under- or overvaluaton,.e., the error term measures the magntude of the under- or overvaluaton. If the error s corrected, the country wll return to the trade balance state. To take nto account of the Balassa-Samuelson effect, we run regresson on GDP per capta. The resultng predcted regresson lne s the means of the RERs of all countres at the same GDP levels. Hence, the devaton from the predcted lne (regresson lne), that s, the resdual term, measures the magntude of under- or overvaluaton of a currency, takng nto account of the Balassa-Samuelson effect.